New methodologies based on frailty models and fraction of cure

Abstract

Several authors have discussed about models with cure fraction. Recently, more complex models have been long exploited in order to better explain the biological mechanisms involved. Models of cure fraction and the usual survival models implicitly assume that all individuals who experienced the event of interest belong to a homogeneous population, however, a way to measure the heterogeneity observed is adding covariates to the model. Thus, a portion of the heterogeneity can be explained by the covariates, however, there is one degree of heterogeneity induced unobservable risk factors. The models that incorporate unobservable heterogeneity between individuals are known as models of frailty. The study proposed in this project is related specifically to research on "Modeling for Data with Survival Fraction Fragility and cure" 'with an emphasis on three sub-projects: 1) A new method of Birnbaum-Saunders distribution as models of frailty; 2) The Model Kumaraswamy-G Long Term; 3) Models with cure rate frailty models based on Winer process for the first passage time. (AU)